Dead simple option: smart outlet connected to ST and a dumb radio. Plug the radio into the outlet. Create a routine: IF mobile presence is present (precondition) AND time is 6:00 am, turn outlet on, turn off automatically after 30 minutes.
Create another routine: IF mobile presence leaves, turn outlet off.
Echo Dot option:
Create a virtual Alexa Switch (link below) I’ll call “Virtual Alarm” and choose the setting to create the linked contact device. Turn the switch on and off with the same logic above. In the Alexa app, create two more routines:
If Virtual Alarm Contact opens, play playlist / radio station / etc. on Bedroom Dot.
If Virtual Alarm Contact closes, stop music on Bedroom Dot.
Neither of these uses your fancy Bluetooth speaker but unfortunately it’s not a good fit for automation. You could maybe plug it into a smart outlet and kill power when you walk away, but I don’t know how that will go for re-syncing the time.